Nonlinear stochastic differential equations and 1/f noise
Nonlinear stochastic differential equations and 1/f noise
Nonlinear stochastic differential equations and 1/f noise
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Connection with other <strong>equations</strong><br />
For some choces of parameters our SDE takes the form of well-known<br />
<strong>equations</strong>.<br />
η = 0 <strong>and</strong> σ = 1 corresponds to the Bessel process<br />
of dimension δ = 1 − ν<br />
dx = δ − 1<br />
2<br />
1<br />
x dt + dW t<br />
η = 1/2, σ = 2 corresponds to the squared Bessel process<br />
of dimension δ = 2(1 − ν)<br />
dx = δdt + 2 √ x dW t<br />
Julius Ruseckas (Lithuania) <strong>Nonlinear</strong> <strong>stochastic</strong> <strong>differential</strong> <strong>equations</strong> August 28, 2012 18 / 32